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A097786 a(n)=3a(n-1)+C(n+3,3),n>0, a(0)=1. 3
1, 7, 31, 113, 374, 1178, 3618, 10974, 33087, 99481, 298729, 896551, 2690108, 8070884, 24213332, 72640812, 217923405, 653771355, 1961315395, 5883947725, 17651844946, 52955536862, 158866612886, 476599841258, 1429799526699 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A052150.

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).

FORMULA

G.f. : 1/((1-3x)(1-x)^4); a(n)=3^(n+4)/16-(4n^3+42n^2+152n+195)/48; a(n)=sum{k=0..n, binomial(n+4, k+4)2^k}.

a(0)=1, a(1)=7, a(2)=31, a(3)=113, a(4)=374, a(n)=7*a(n-1)- 18*a(n-2)+ 22*a(n-3)-13*a(n-4)+3*a(n-5) [From Harvey P. Dale, Nov 26 2011]

MATHEMATICA

RecurrenceTable[{a[0]==1, a[n]==3a[n-1]+Binomial[n+3, 3]}, a, {n, 30}] (* or *) LinearRecurrence[{7, -18, 22, -13, 3}, {1, 7, 31, 113, 374}, 31] (* Harvey P. Dale, Nov 26 2011 *)

CROSSREFS

Sequence in context: A205492 A109756 A055580 * A197649 A006458 A091344

Adjacent sequences:  A097783 A097784 A097785 * A097787 A097788 A097789

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 24 2004

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)